Final Answer
Step-by-step Solution
Specify the solving method
Divide $x^3+2$ by $x^2-2x+2$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{2}-2x\phantom{;}+2;}{\phantom{;}x\phantom{;}+2\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-2x\phantom{;}+2\overline{\smash{)}\phantom{;}x^{3}\phantom{-;x^n}\phantom{-;x^n}+2\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+2;}\underline{-x^{3}+2x^{2}-2x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{3}+2x^{2}-2x\phantom{;};}\phantom{;}2x^{2}-2x\phantom{;}+2\phantom{;}\phantom{;}\\\phantom{\phantom{;}x^{2}-2x\phantom{;}+2-;x^n;}\underline{-2x^{2}+4x\phantom{;}-4\phantom{;}\phantom{;}}\\\phantom{;-2x^{2}+4x\phantom{;}-4\phantom{;}\phantom{;}-;x^n;}\phantom{;}2x\phantom{;}-2\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^3+2)/(x^2-2x+2))dx. Divide x^3+2 by x^2-2x+2. Resulting polynomial. Expand the integral \int\left(x+2+\frac{2x-2}{x^2-2x+2}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int xdx results in: \frac{1}{2}x^2.